Precalculus Examples

$\log (\frac{x}{y}) = \frac{\log (x)}{\log (y)}$

Step 1

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 10$ , $x = \frac{x}{y}$ , and $y = \frac{\log (x)}{\log (y)}$ .

$b = 10$

$x = \frac{x}{y}$

$y = \frac{\log (x)}{\log (y)}$

Step 2

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

$10^{\frac{\log (x)}{\log (y)}} = \frac{x}{y}$